Question

Using data from the previous table, construct an exponential model for this situation.A ( t ) =What will be the value when t=8, rounded to 2 decimal places?

Answer 1

• Exponential model

`A(t)=13.60(1+0.25)^(t)`
`A(8)\approx81.06`

Step-by-step explanation

The exponential model equation can be given by:

`A(t)=C(1+r)^t`

where C is the initial value, r is the rate of growth and t is the time.

We can get the initial value by evaluating in the table when t = 0. In this case the value A(0) = 13.60. Then our equation is:

`A(t)=13.60(1+r)^t`

Now we have to get r by choosing any point and solving for r. For example, (3, 26.56). By replacing the values and solving we get:

`26.56=13.60(1+r)^3`
`(26.56)/(13.60)=(1+r)^3`
`(1+r)^3=(26.56)/(13.60)`
`\sqrt[3]{(1+r)^3}=\sqrt[3]{(26.56)/(13.60)}`
`1+r=\sqrt[3]{(26.56)/(13.60)}`
`r=\sqrt[3]{(26.56)/(13.60)}-1\approx0.2500`

Thus, our rate is 0.25, and we can add it to our equation:

`A(t)=13.60(1+0.25)^t`

Finally, we evaluate t = 8:

`A(8)=13.60(1+0.25)^8=81.06`